function toggleInputs() {
var method = document.getElementById('calcMethod').value;
var angleGroup = document.getElementById('angle_group');
var labelA = document.getElementById('labelA');
var labelB = document.getElementById('labelB');
if (method === 'lawCosines') {
angleGroup.style.display = 'block';
labelA.innerText = "Length of Known Side 1:";
labelB.innerText = "Length of Known Side 2:";
} else if (method === 'pythagorasLeg') {
angleGroup.style.display = 'none';
labelA.innerText = "Length of Hypotenuse (c):";
labelB.innerText = "Length of Known Leg (a or b):";
} else {
angleGroup.style.display = 'none';
labelA.innerText = "Length of Side A:";
labelB.innerText = "Length of Side B:";
}
}
function calculateTriangle() {
var method = document.getElementById('calcMethod').value;
var a = parseFloat(document.getElementById('sideA').value);
var b = parseFloat(document.getElementById('sideB').value);
var angle = parseFloat(document.getElementById('angleC').value);
var result = 0;
var formula = "";
if (isNaN(a) || isNaN(b) || (method === 'lawCosines' && isNaN(angle))) {
alert("Please enter valid numeric values for all required fields.");
return;
}
if (method === 'pythagoras') {
result = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2));
formula = "Using Pythagoras: √(a² + b²) = √(" + a + "² + " + b + "²)";
} else if (method === 'pythagorasLeg') {
if (a <= b) {
alert("Hypotenuse must be longer than the known leg.");
return;
}
result = Math.sqrt(Math.pow(a, 2) – Math.pow(b, 2));
formula = "Using Pythagoras: √(c² – b²) = √(" + a + "² – " + b + "²)";
} else if (method === 'lawCosines') {
var angleRad = angle * (Math.PI / 180);
result = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) – (2 * a * b * Math.cos(angleRad)));
formula = "Using Law of Cosines: √(a² + b² – 2ab cos(C))";
}
document.getElementById('resultArea').style.display = 'block';
document.getElementById('calcOutput').innerText = "Missing Side = " + result.toFixed(4);
document.getElementById('calcFormula').innerText = formula;
}
How to Calculate Triangle Sides: A Complete Guide
Understanding how to calculate the length of triangle sides is a fundamental skill in geometry, trigonometry, and various real-world applications like construction, navigation, and engineering. The method you use depends entirely on the information you currently have and the type of triangle you are dealing with.
1. The Pythagorean Theorem (Right-Angled Triangles)
If you are working with a right triangle (one angle is exactly 90 degrees), the most common tool is the Pythagorean Theorem. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
a² + b² = c²
- Finding the Hypotenuse (c): Calculate c = √(a² + b²)
- Finding a Leg (a or b): Calculate a = √(c² – b²)
2. The Law of Cosines (Any Triangle)
When you are not dealing with a right triangle, or if you only know two sides and the angle between them (Side-Angle-Side or SAS), the Law of Cosines is your best option. It is essentially an extension of the Pythagorean Theorem that works for all triangles.
c² = a² + b² – 2ab cos(C)
Where a and b are the known sides, and C is the angle between them.
Practical Examples
Example 1: Right Triangle Hypotenuse
If Side A is 3 and Side B is 4, then:
c = √(3² + 4²) = √(9 + 16) = √25 = 5.
Example 2: Using the Law of Cosines
Suppose you have two sides of 10 and 15, with a 60-degree angle between them.
c² = 10² + 15² – 2(10)(15) cos(60°)
c² = 100 + 225 – 300(0.5) = 325 – 150 = 175
c = √175 ≈ 13.23.
Summary Table of Formulas
| Scenario |
Formula to Use |
| Right Triangle (Known 2 legs) |
c = √(a² + b²) |
| Right Triangle (Known Hypotenuse + 1 leg) |
a = √(c² – b²) |
| Any Triangle (SAS) |
Law of Cosines |
| Any Triangle (ASA or AAS) |
Law of Sines |